We incorporate information about the physical structure of the footprint in determining the structure of the Gaussian field \(\lbrace \tilde{X}^G (s,t) : s \in \mathcal {E}_t\rbrace \)  by using conditional simulation [1]}. We impose three conditions on the simulated fields: that the maximum relative wind speed is simulated at the position determined by \(R^{W}_t\)  and \(\Theta ^{W}_t\) ; that the lower limit of \(\tilde{D}_t\)  occurs on the outer perimeter of the ellipse; and that the lower limit of \(\tilde{D}_t\)  occurs everywhere in the region corresponding to the local minimum of wind speeds (see Section REF ) near the storm centre when a footprint is simulated in the vicinity of this region. The first and second conditions create a two-dimensional pseudo-Brownian bridge between the position of maximum and the perimeter of the footprint. To impose the third condition, we specify a second ellipse centred at the local minimum with random dimensions for size; specifically we fix the maximum length of the semi-major and semi-minor axes of this ellipse to be 40 and 35 units of grid-cell distance respectively, with random perturbations modelled as Exp(0.05) random variables. These values were found to replicate well the average behaviour of wind speeds in the region at which the local minimum occurs.
